How to recreate the pixel effect that happens when you move rendered objects
It's not terribly clear what you are hoping for, but what I believe you are asking is how to sample the image in such a way that results in that blocky look.

You should be able to effectively get a similar result using the Transform node in the compositor. Simply:


Resample the image to be a very low resolution version of the input image using Nearest sampling and the Scale value. For example, sample your image from 100 pixels by 100 pixels down to 10 pixels by 10 pixels.
Resample the image back to the original resolution using nearest and the scale value again.


Combinations of the above may be required if you are animating, to control the smoothness of the motion. Nearest will literally find the nearest sampled point and can result in very blocky movement, while a combination of nearest with linear may smooth things out. You can see a sample of the effect used in this music video from several years ago, achieved with a custom bit of node code as nearest wasn't available.